We are delighted to welcome Philippe Borer back to The Exhale with his popular series 'How to Play in Tune' and his examination of the concept of intonation. Since 2007 Philippe Borer has been conducting masterclasses on violin intonation, notably at the Novgorod State University, the Mozarteum Salzburg and the University of Alberta. Come and join him for these seven 45 minute classes as he takes us through 'How to Play in Tune'. Practical exercises with active participation, as well as the study of relevant passages from the violin repertoire, will form the core of classes 3 to 7. The theoretical part will be made available to the participants in written form before each class.
Class I | Playing in Tune
In this class, Philippe investigates the musical idea of 'playing in tune'. Tune and intonation (Intonation, intonazione, intonation, интонация) derive from the Sanskrit तान (tāna) which means 'thread', 'fiber', 'tone', 'vibration', 'tension of a string', 'tuning up', 'extension of knowledge'. तान was imported in Greek as τόνος, meaning rope, string, strength, tension, and specifically, the tension of the strings of the lyre. In its broader sense, τόνος referred to the tones produced by a music instrument. The Greeks saw the physical body as a kind of musical instrument where each string must have the right tension. Therefore, the term was used in medicine as well (for example, 'tone', 'tonic', 'well-tempered, etc.) The Latin form of τόνος is tonus. Significantly, the Latin word 'intentio', the French word 'entendre' and the Italian 'intendimento' also have their origin in τόνος and तान. The class ends with a discussion and all attendees may express their views on musical intonation.
Class 2 | the First 256 Overtones
Today's class aims to construct the table of the first 256 overtones. This requires intense concentration from all but it is a passage obligé. The table allows to visualise the ratios and sizes of the musical intervals and gives an insight into the correspondence between number and tone. It is immensely helpful while studying music treatises (including Tartini, Vallotti, Rameau and even sources such as Plato's musical allegories or the remote Sāmaveda). The process of constructing the table is conducive both to an understanding of the traditional notation and of its shortcomings, in particular the ambiguity of notating two different sound-numbers in the same way on the musical staff.
Class 3 | Solving the Ambiguities of Staff Notation
Our system of notation was originally devised with Pythagorean intonation in mind. The previous class has shown that a problem of notation already arises with overtone 5. In fact every new prime number introduces tonal relationships that can no longer be accurately represented with the ordinary notation. The use of comma signs (ascending and descending slashes as well as the Tartini arrow) helps to dispel the ambiguities.
Class 4 | Tuning strategies
Today Philippe focuses on some paradoxes pertaining to violin intonation and tuning. In his treatise of 1797 Galeazzi states that “there are instances where, in order to have your Violin well in tune, you have to adjust it out of tune”. He suggests to adapt the tuning of the violin to the key of the piece, using a procedure which could be defined as comma scordatura. Paganini too seems to have practised, besides the scordatura proper, a kind of sophisticated adjustment of the fifth tuning. The problem of bow pressure and its relation to pitch will be examined and the attendees will be invited to experiment with two distinct modes of string vibration, the régime libre (free vibration) and the régime contraint (forced vibration).
Class 5 | Formation of the fundamental scale
In their theoretical writings Tartini and Galeazzi stated that the reference scale on the violin was the syntonic diatonic scale and gave its formula with proportional ratios, relative string lengths and implicit frequency ratios. Both maintained that they did not use temperament. In particular, Tartini rejected the idea of altering the proportions of the fundamental scale, noting that this was not necessary on the violin. Be that as it may, it is evident that the proportional system is primary, not only from a philosophical or historical point of view, but because it is inscribed in the vibration of the string itself. The temperament, on the other hand, is an alteration of the fundamental proportions, “a distortion for the sake of convenience or necessity”(Norden). In fact, for the violinist, starting from a temperament, whatever it is, would mean reversing the terms of the problem. Tartini discovered that the intervals of the fundamental scale can be measured with absolute precision on the violin. His method was to establish the exact relationship with the tonic through the control of the difference tone (terzosuono). The 'third sound', true compass of the ear, allows the player to determine the numerical ratio of each successive interval with the greatest accuracy. One could say that the intervals reveal themselves to the player via their difference tones. The class ends with exemplification and practical exercises.
Class 6 | Paganini's Scale
Paganini's scale, also known as the 'harmonic chromatic scale', is a master scale containing all the essential tone relations. Its particular tone arrangement fits the concept of melody as 'harmony in succession' defined by Tartini and Vallotti. Such a notion, almost completely ignored today, was still relevant to Paganini and to those violinists who had trained in the grand tradition of Corelli, Tartini, Somis, Locatelli, Geminiani, Leclair, Nardini, Cambini, Pugnani, Campagnoli, Galeazzi, and Viotti. Paganini, unanimously praised for the purity and the unerring accuracy of his intonation, followed the principles of Tartini. Scales and melodies united to the tonic (often as an open string drone) abound in his work. The astonishing quality of Paganini's intonation was due to the polyphony of consecutive notes in syntonic relationship with each other. The class opens with an analysis of Paganini's scale based on Euler's harmonic network (the Speculum Musicum) followed by practical exemples, exercises and a concluding debate.
Class 7 | The expressive value of musical intervals
It is in music that we can directly perceive mathematical relationships that we feel as expressive values, ideas, movements, and aesthetic flavours (rasa). Today's class focuses on the contrasting expressive values and flavours of the following intervals: the third 4/5 ( ‘pure’), the third 64/81 (‘heroic’), the minor third 5/6, the septimal third 6/7, the diminished third 225/256 (‘nostalgic’), the augmented third 512/675 (‘emotional’) and Tartini's minor third 27/32
Classes held via zoom, limited to small numbers. This event has multiple classes.
Missed a class? You can still purchase a ticket to access the recording.
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